Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, m, d, y;
  cin >> n;
  long long cnt = 0;
  vector<long long> v;
  long long i = 1;
  while (cnt < 1000000001) {
    cnt += i;
    v.push_back(cnt);
    i++;
  }
  if (n == 1) {
    cout << "NO"
         << "\n";
    return 0;
  }
  auto itr = lower_bound(v.begin(), v.end(), n - 1);
  if (*itr == n) itr--;
  while (*itr > 0) {
    y = n - (*itr);
    auto itr1 = lower_bound(v.begin(), v.end(), y);
    if (*itr1 == y) {
      cout << "YES"
           << "\n";
      return 0;
    }
    if (*itr == 1) break;
    itr--;
  }
  cout << "NO"
       << "\n";
  return 0;
}